How would I pick $a,b,c$ to create a line that is parallel to $z$-axis and intersects $x$-axis at point $x=k, y=0, z=0$?
$$ ax+by+cz=d $$
2026-04-01 15:59:04.1775059144
Equation for line parallel to z-axis and intersects x-axis at (x=k, y=0, z=0)
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Since, line passes through (k,0,0) and is parallel to z-axis so, the equation of line is $(x,y,z) = (k,0,0) + \alpha$(0,0,1), $\alpha \epsilon \mathbb{R}$